Ingredients

• 4 slices thick white country bread
• 2 tablespoons unsalted butter, divided
• 1 tablespoon all-purpose flour
• 1/2 cup whole milk
• 1/4 teaspoon ground nutmeg
• 4 thin slices cooked ham
• 1 cup grated Gruyère cheese, divided
• 2 large eggs

Steps

1. Melt 1 tablespoon of unsalted butter in a small saucepan over medium heat, whisk in 1 tablespoon of all-purpose flour, and cook for 1 minute.
2. Slowly whisk in 1/2 cup of whole milk until smooth, then season with 1/4 teaspoon of ground nutmeg and remove from the heat.
3. Lay out the 4 slices of country bread on a baking sheet and spread a thin coat of warm béchamel over each slice.
4. Place 2 slices of cooked ham and 1/4 cup of grated Gruyère on each of 2 bread slices, then cap them with the remaining bread slices.
5. Spread the remaining béchamel over the tops, sprinkle with the remaining 1/2 cup of grated Gruyère, and broil at 400°F [200°C] for 5 to 7 minutes until bubbling.
6. Melt the remaining 1 tablespoon of unsalted butter in a skillet, fry the 2 large eggs sunny-side up, and place one egg atop each sandwich.